Finding length and longitudinal magnification

1. The problem statement, all variables and given/known data
A small object of length dL is placed on the axis of a converging mirror of focal length f. The center of the object is a distance o from the mirror. Determine the length of the image and thus effective determine a longitudinal m' = dL'/dL for the lens.

2. Relevant equations

3. The attempt at a solution

I know that the distance from the center to the object to the mirror is o so one end of the mirror is o+dL/2 and the other end is o - dL/2. I will call x = o + dL/2 and y = o -dL/2

The correct answer is m'=-m^2. By definition, m = -i/o. I don't see how to get this. Did I approach the problem incorrectly or am I overlooking some kind of algebra manipulations? How do I get to -m^2?